As a motivating example, we consider the Framingham Heart Study [1]}. The Framingham Heart Study is a large cohort study investigating coronary heart disease. Following previous analyses in the measurement error literature [2]}, our interest concerns the impact of long-term average systolic blood pressure on the development of coronary heart disease, while controlling for other risk factors. Systolic blood pressure is considered error-prone since it is a single time point measurement which may differ substantially from the long-term average blood pressure. The study reports four separate measurements of systolic blood pressure, two at each clinical visit, from two visits four years apart. Analyses of these data often consider these four measurements as replicated measurements of the same underlying value [2]}. That is, the systolic blood pressure measurements are considered independent and identically distributed realizations of the same variable. While this assumption is a reasonable approximation, [2]} note that these sets of measurements deviate substantially from one another. This is the setting our techniques are developed for.
